Published German patent application 101 33 588 A1 discloses a semiconductor chip arranged on a chip carrier and an antenna. The chip carrier and the antenna have each conductive surfaces, which are glued together by means of a non-conductive glue layer, so that the conductive surfaces are coupled capacitively. The conductive surfaces and the intermediate non-conductive glue layer constitute capacitors whose capacitances are determined, inter alia, by the thickness of the glue layer. The glue layer, however, cannot be applied accurately within a certain thickness, resulting in varying capacitances of different chips including the antenna.